The subject matter discussed in the background section should not be assumed to be prior art merely as a result of its mention in the background section. Similarly, a problem mentioned in the background section or associated with the subject matter of the background section should not be assumed to have been previously recognized in the prior art. The subject matter in the background section merely represents different approaches, which in and of themselves may also be inventions. There are a variety of numerical techniques for computing numerical fields. Boundary element methods are often used in electromagnetic simulations. The general idea is that space is modeled as consisting of regions with uniform electromagnetic response properties separated by negligibly thin boundaries. For each uniform region, a parameterized solution to Maxwell's equations is written (for example, a sum of parameters times plane waves, or a sum of parameters times fields due to fictitious “equivalent sources”). The parameterization and the parameters are chosen so that the error is small in some sense.
However, the best method for minimizing the errors is not at all obvious. A common method is the “method of moments.” However, the method of moments is rather poorly motivated and ad-hoc. Different choices of parameters are chosen for different (and rather poor) notions of “error” and “small” for different situations. In other words, the choice of parameterization and parameters is an art form that depends on the user's intuition.